FSI with solid contact in the fluid domain

I've been trying to simulate a simple problem of a sphere moving in a stagnant fluid domain. The sphere come into contact with a solid object and deforms.

Problem #1) In any contact problem, the gap between the object becomes zero. This creates inverted mesh in the fluid domain between the contacting bodies. What is the solution for this? The solver gets stuck because of inverted mesh warning in the contact zone.

Problem #2) In the solid mechanics node of the FSI, if a prescribed displacement is defined, it will overwrite the fluid-solid boundary condition. This is a very limiting! My solid problem is entirely displacement oriented with displacement defined on boundaries. Does anyone has a recommendation for this?

The model is attached.

Thanks for helping out!